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A county's population in 1991 was 147 million. In 1998 it was 153 million. Estimate the population in 2017 using the exponential growth formula. Round your answer to the nearest million.

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  1. 8 July, 16:49
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    Let t=number of years since 1991.

    Then

    P (t) = 147 e^ (kt) ... in millions

    P (0) = 147 e^ (0) = 147

    P (7) = 147 e^ (7k) = 153

    e^ (7k) = (153/147)

    take ln both sides

    ln (e^ (7k)) = ln (153/147)

    7k=0.0400 = > k=0.005715

    Year 2017=>t=2017-1991=26

    P (26) = 147e^ (26*.005715) = 170.55

    Answer: in 2017, the projected population is 170.55 millions.
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